A034305 Zeroless nonprimes that remain nonprime if any digit is deleted.

14, 16, 18, 44, 46, 48, 49, 64, 66, 68, 69, 81, 84, 86, 88, 91, 94, 96, 98, 99, 122, 124, 125, 126, 128, 142, 144, 145, 146, 148, 152, 154, 155, 156, 158, 162, 164, 165, 166, 168, 182, 184, 185, 186, 188, 212, 214, 215, 216, 218, 221, 222, 224, 225, 226, 228

Offset

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Mathematica

npQ[n_]:=!PrimeQ[n]&&FreeQ[IntegerDigits[n], 0]&&AllTrue[FromDigits/@ Table[Drop[IntegerDigits[n], {k}], {k, IntegerLength[n]}], !PrimeQ[#]&]; Select[Range[10, 300], npQ](* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 19 2021 *)

Prog

(Haskell)
a034305 n = a034305_list !! (n-1)
a034305_list = filter f $ drop 9 a052382_list where
  f x = a010051' x == 0 &&
        (all (== 0) $ map (a010051' . read) $
         zipWith (++) (inits $ show x) (tail $ tails $ show x))
-- Reinhard Zumkeller, May 10 2015
(PARI) is(n)=my(d=digits(n)); if(#d<2 || vecmin(d)<1 || isprime(n), return(0)); for(i=0, #d-1, if(isprime(fromdigits(vecextract(d, 2^#d-1-2^i))), return(0))); 1 \\ Charles R Greathouse IV, Jun 25 2017
(Python)
from sympy import isprime
def ok(n):
    if n < 10 or isprime(n): return False
    s = str(n)
    return "0" not in s and not any(isprime(int(s[:i]+s[i+1:])) for i in range(len(s)))
print([k for k in range(229) if ok(k)]) # Michael S. Branicky, Jan 15 2023

Crossrefs

Subsequence of A052382.

Cf. A034302, A034303, A034304, A010051.

Sequence in context: A053425 A178071 A177982 * A091898 A061365 A327822

Adjacent sequences: A034302 A034303 A034304 * A034306 A034307 A034308

Keyword

base,nonn,nice

Author

David W. Wilson

Extensions

Definition corrected by T. D. Noe, Apr 02 2008

Single-digit terms removed again by Georg Fischer, Jun 21 2021

Status

approved